I am so sorry that you are going through this, I have been there too 
From your posts it seems to me that the way you are feeling is that you want to confront him and pull him up on things but you dare not be to harsh about it in case it forces him to leave or into the arms of the other woman.
The crux of this for me is that ultimately you keep giving him the upper hand, and what I mean by this is your acting like your the one who has got so much to lose (and of course I know you have, and that you want to keep your family together) like your the one on the back foot and you are showing him all your weaknesses by behaving like this and he is just taking advantage by spinning you more lies and taking this EA deeper underground. He is the one that should be running around scared out of his mind that he is going to lose YOU, he is the one that should be feeling that HE is on the back foot, HE should be worrying about YOU not worrying about himself!!! For your own sanity you need to put a stop to this asap before your self respect and self esteem ebb away into nothing.
You need to start showing him the hard line here, you need to start showing him that HE is the one that has got so much to lose, you need to make it real in his mind that HE WILL lose you if he chooses to continue what he is doing. You need to command his respect and not wait for him to give it to you, you need command full disclosure on this affair and you need to command that it STOP RIGHT NOW! These are all things that you deserve!!! Show him that you will not accept anything less than love, respect and truth....because if he cant give you these things you relationship is doomed to fail at some point in the future anyway.
If I were you (having learned from bitter experience) in reality you do not need all the details or even proof that he is doing all the things you suspect. You have enough proof and lies told to you by him to know indeed what is going on, you do not need an admission from him to deduce that (although it is nice to get I understand) your a smart woman so stop letting him insult your intelligence by continuing to let him feed you lies upon more lies. I would tell him that you have simply had enough, had enough of all the lies, all the excuses and that you feel you are simply not getting the truth. I would tell him that you deserve more, that you and your children deserve more. I would say that you are not sure that he is the man you once knew and trusted and that until you get the whole truth that you want him to leave for a while so you can have some space to think about the kind of man he has become and if he is even worthy of your time and affections anymore.
Say it....and then stick to your guns....do not crumble. By making this totally and entirely real for him is the only way his is going to get a big slap of reality and truly realise what he is got at stake here and what he is losing. Once you get him to do this, then you have the position of power (crude as it may sound) but that is what you need in order to set the ground rules of your relationship continuing/repairing. He has to become really and truly sorry for what he has done in order for you to be able to move forward, and right now he is not sorry, he is only sorry he got caught out because all his doing in continuing to tell you lies and carrying on with his little affair....just what he wants!!! Its up to you to make him sorry, its up to you to make him see, make him understand what and wonderful woman (and you are a wonderful woman) and wonderful family he has to lose. Yes there is the possibility he wont wake up and yes there is the possibility that he chooses the other woman (its very unlikely trust me) but if that is the case than the stupid idiot of a man was not worth having anyway....because he was not worthy of you!!!
Sorry that was long, but I hope it helps.